bringing bioelectricity to lightcohenweb.rc.fas.harvard.edu/publications... · bringing...

BB43CH10-Cohen ARI 12 May 2014 15:38

Bringing Bioelectricity to LightAdam E. Cohen1,2 and Veena Venkatachalam3

1Department of Chemistry and Chemical Biology and 2Department of Physics,3Program in Biophysics, Harvard University, Cambridge, Massachusetts 02138;email: [email protected], [email protected]

Annu. Rev. Biophys. 2014. 43:211–32

First published online as a Review in Advance onApril 24, 2014

The Annual Review of Biophysics is online atbiophys.annualreviews.org

This article’s doi:10.1146/annurev-biophys-051013-022717

Copyright c© 2014 by Annual Reviews.All rights reserved

Keywords

membrane voltage, optogenetics, electrophysiology

Abstract

Any bilayer lipid membrane can support a membrane voltage. The com-bination of optical perturbation and optical readout of membrane voltageopens the door to studies of electrophysiology in a huge variety of systemspreviously inaccessible to electrode-based measurements. Yet, the applica-tion of optogenetic electrophysiology requires careful reconsideration of thefundamentals of bioelectricity. Rules of thumb appropriate for neuroscienceand cardiology may not apply in systems with dramatically different sizes,lipid compositions, charge carriers, or protein machinery. Optogenetic toolsare not electrodes; thus, optical and electrode-based measurements have dif-ferent quirks. Here we review the fundamental aspects of bioelectricity withthe aim of laying a conceptual framework for all-optical electrophysiology.

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Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212WHAT GENERATES MEMBRANE VOLTAGE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Membrane Voltage at Thermal Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214Nonequilibrium Membrane Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

WHY DOES MEMBRANE VOLTAGE MATTER?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221PATCH CLAMP VERSUS OPTOGENETICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Perturbing Membrane Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223Measuring Membrane Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

THE FUTURE OF OPTICAL ELECTROPHYSIOLOGY. . . . . . . . . . . . . . . . . . . . . . . . 226Reporters of Absolute Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Voltage Integrators and Voltage Samplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

INTRODUCTION

Bioelectric phenomena are ubiquitous. Lipid membranes are insulators bathed in a conductingmilieu. Any lipid membrane can, in principle, support a transmembrane electric field and thus avoltage difference between its faces. The electric field tugs on charges in the membrane; thesecharges may be in lipid head groups, transmembrane proteins, or membrane-embedded redoxmolecules. Membrane voltage modulates the free-energy landscape of all molecules associated withthe membrane. Any statement about the kinetics or thermodynamics of a membrane-associatedprocess must specify the membrane voltage.

This simple fact has wondrous and far-reaching implications. The importance of membranevoltage is well appreciated in neurons and cardiomyocytes, both of which produce fast and large-amplitude electrical spikes. But the association of electrophysiology with these two cell types isalso partly a consequence of how we measure membrane voltage. For electrode-based measure-ments the cell must be mechanically accessible, nonmotile, and large enough to impale. Patchclamp connections tend to degrade over time, so fast spikes are easier to measure than long-termshifts in baseline voltage. Many membrane-bound structures are inconvenient or impractical tomeasure with electrodes and thus have been little studied from an electrophysiological perspective.Examples are membrane-enveloped viruses (24), cellular organelles [mitochondria (44), nuclearmembrane (53), endoplasmic reticulum (76), and the many types of intracellular vesicles], mi-croorganisms [bacteria (21, 47, 51), yeast (32)], motile cells [sperm (45), amoeboid slime molds(60), immune cells (13)], cells with a cell wall [plants (91) and fungi (79)], and tissues undergoingmorphogenesis [developing embryos (85), healing wounds (64)]. The limited experimental dataavailable suggest that in most of these systems, voltage is dynamically regulated. Yet our ability toexplore the role of voltage has, until recently, been constrained by available tools.

With the advent of new optical approaches for measuring and perturbing membrane voltage,we argue that the time has come for a renaissance in the study of bioelectricity in these “uncon-ventional” systems. In embarking on such a study, one must reexamine the fundamental tenetsof electrophysiology in the context of different physical parameters: Well-established intuitionsappropriate for neuronal electrophysiology might not apply to systems with dramatically differentsizes (see sidebar, Electrophysiology in Small Systems), lipid compositions, ionic environments,

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ELECTROPHYSIOLOGY IN SMALL SYSTEMS

Optical voltage measurements could be applied to vesicles (endocytic or secretory), lipid-enveloped viruses, andbacteria. An indication of the surprises waiting in this domain comes from optical measurements of membranevoltage in bacteria. Escherichia coli expressing a proteorhodopsin-based optical voltage indicator (PROPS) showeddiverse electrical spiking behaviors that responded sensitively to ionic and pharmacological perturbations (47).

However, electrophysiology in prokaryotes likely differs from that in eukaryotes. The membrane capacitanceof a bacterium is between 10−14 and 10−13 F (assuming a specific capacitance of 1 μF/cm2 and typical bacterialdimensions). A single ion channel opening with a conductivity of 100 pS can alter the membrane potential with atime constant of 10−3–10−4 s. In contrast, neurons only fire through the concerted action of a large number of ionchannels.

Additionally, because of their small volume, prokaryotes have a less robust ionic composition than do eukaryotes.A bacterium with a volume of 1 fL and a cytoplasmic Na+ concentration of 10 mM contains only ∼107 atoms of Na+.A single ion channel passing a current of 2 pA can deplete this store in less than 1 s. Finally, the number of channelsof any particular type might be countably small. Stochastic insertion or degradation events or posttranslationalmodifications might qualitatively change the electrophysiological state of a cell. These simple estimates show thatone may need to rethink many of the tenets of neuronal electrophysiology in the context of prokaryotes.

and/or protein machinery. One can expect a variety of new phenomena to arise in the context ofunconventional electrophysiology.

Technical aspects of optical electrophysiology also differ from conventional patch clamp inseveral subtle but critically important ways. In whole-cell patch clamp, the patch pipette pro-vides a near infinite reservoir in diffusive contact with the cytoplasm. Dialysis of cellular contentscan suppress naturally occurring changes in cytoplasmic composition. In contrast, the cell mem-brane remains intact in optogenetic electrophysiology, so natural compositional fluctuations arepreserved. In addition, current injection from the patch pipette does little to directly influencecellular composition in patch clamp electrophysiology, whereas for optogenetic currents, eachionic species must individually achieve mass balance across the cell membrane. Endogenous co-transporters and antiporters can lead to surprising couplings of the optogenetically pumped ionto fluxes of other “bystander” ions.

Patch clamp and optical electrophysiology are fundamentally different in that they measuredifferent things: Patch clamp reports the total voltage drop across the membrane and its as-sociated double layers, whereas optical probes sense local intramembrane electric fields. Thesetwo quantities are related but not identical. Membranes can have strong internal electric fieldsgenerated by asymmetries in ionic environment or lipid composition. These electric fields do notcontribute to the membrane potential as measured by patch clamp, but they can strongly influencemembrane permeability and the conformations of transmembrane proteins. One must remem-ber that the electrostatic potential profile across the membrane cannot be described by a singlenumber; patch clamp and optical techniques report different aspects of the complex potentialprofile.

In this review, we address three questions: What generates membrane voltage? How doesmembrane voltage affect processes in the membrane? What are the challenges and opportunitiesof optical versus electrode-based electrophysiology? As the literature on electrical measurements inunconventional systems spans more than a century and is too vast and scattered to review in depth,we instead highlight a few measurements that illustrate important biophysical principles. Someof this material is discussed in older literature and textbooks (41, 55), but it merits reexamination

www.annualreviews.org • Bringing Bioelectricity to Light 213

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in light of improved technology. Our primary purpose is to encourage the reader to contemplatethe role of membrane voltage in her or his favorite system.

WHAT GENERATES MEMBRANE VOLTAGE?

Membranes can contain diverse ion channels, exchangers, pumps, and redox molecules. How doesone calculate the membrane voltage? Or, of more concern to the experimentalist, what do mea-surements of membrane voltage and its susceptibility to ionic and pharmacological perturbationsteach us about the transporters in the membrane? The Nernst and Goldman equations as typi-cally taught in introductory neurobiology classes encompass only a limited subset of biologicallyimportant scenarios. To understand the full diversity of bioelectric phenomena, we must returnto the basics.

To illustrate the need for a more general approach, let us consider the mitochondrial membranepotential, which has been indirectly inferred to be in the range of −150 to −190 mV (63, 68). Noneof the major ions in mitochondria (H+, K+, Na+, Ca2+) has a concentration gradient strong enoughto generate a Nernst potential of −150 mV. Application of the Goldman equation does not helpbecause the Goldman equation always predicts a membrane voltage that lies between the Nernstpotentials of the individual ions. Furthermore, mitochondria contain ion pumps, ion exchangers,redox couples, and metabolite carriers (68). The associated charge fluxes clearly contribute to themembrane voltage, but the Nernst and Goldman equations as usually written do not accommodatethese types of electric currents.

Tables 1 and 2 show seven physical processes that can generate a membrane voltage, severalof which are often at play simultaneously. We classify these processes into those that occur atthermal equilibrium and those that require a nonequilibrium steady state. Membrane voltages atthermal equilibrium can persist indefinitely, even in the absence of metabolic input (except for thegradual dissipation of ion concentration gradients resulting from leakage through the membrane).In the nonequilibrium scenarios, active ion pumps or exchangers are needed to maintain the con-centration gradients that lead to the voltage. For a lucid discussion of some of these mechanisms,the reader is referred to Reference 41.

Membrane Voltage at Thermal Equilibrium

Consider an arbitrary charge-transfer process across a membrane. For the moment, let us restrictour discussion to a single concerted reaction for which membrane voltage influences the reactionrate. Thermal equilibrium occurs when the voltage is such that the forward and reverse rates areequal. The net transport of charge across the membrane is then zero, and the net transport ofeach species is also zero. Basic thermodynamics tells us that the membrane potential at thermalequilibrium is

V in−out = V 0 + RTzF

ln Q, 1.

where V0 is the membrane potential that would exist if all species were in their standard states(1 M activity, 25◦C), z is the number of positive charges transferred from the inside to the outsideper reaction cycle, F is the Faraday constant (the electric charge of one mole of protons), andQ is the reaction quotient (product concentrations raised to their stoichiometric coefficients andmultiplied, divided by reactant concentrations, raised to their stoichiometric coefficients and mul-tiplied). (In the electrochemistry literature, the sign on the second term is reversed because oneis usually dealing with electrons; here we consider positively charged ions.) At room temperature(22 ◦C) and z = 1, Equation 1 implies a decrease in V of 58.6 mV for every tenfold decrease in Q.


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Table 1 Membrane voltages at thermal equilibrium

Physical scenario Schematic ExamplesSingle permeable ion B+

A+

Approximate resting potential in neurons and Tlymphocytes (13, 12)

Coupled transport of multiple ions;coupled transport of ions and metabolites mB+

nA+

ClC chloride/proton antiporters (1), NhaAsodium/proton antiporter (86), NCXsodium/calcium antiporter (6)

Coupled transport of ions and a chemicalreaction

nA+

C

B

F0F1 ATPase (62), Na+/K+ ATPase

Redox reaction

A+

A

B–

e–

B

Oxidative phosphorylation in bacteria,mitochondria, and chloroplasts (62); oxidativeburst in phagocytes (4, 20, 77) and some plantplasma membranes (72)

Donnan potential: single impermeable ion

A+

B+

Vertebrate skeletal muscle (36), erythrocytes(26, 37), nuclear envelope (53), some viral capsids(88), and cartilage (50)

Any chemical transformation that transports charge across a membrane reaches thermal equilibrium when the thermodynamic driving force of thereaction balances the change in electrostatic energy of the transported charge. The driving force can come from diffusion, chemical reactions, or redoxreactions. Each reaction scheme is described in detail in the main text.

Although Equation 1 is familiar to any student of introductory electrochemistry, its implicationsfor bioelectricity are often underappreciated.

Nernst. In the simplest case, a membrane is solely permeable to a single ion. For instance, thereaction could be K+

in ↔ K+out via the Kv1.3 voltage-gated potassium channel found in human T

lymphocytes (13, 12). Here z = 1. There are no chemical transformations, so V0 = 0. Equation 1then reduces to the Nernst equation as usually written in neuroscience textbooks:

V in−out = RTzF

lnCout

Cin. 2.

Thermal equilibrium is reached when the electrostatic driving force is just strong enough tocounteract the tendency of K+ ions to diffuse from a high concentration to a low concentration.

Coupled transport. Symporters and antiporters couple transport of multiple species with a well-defined stoichiometry and sometimes with a net transport of charge. Examples include the mam-malian chloride transporters ClC-4, ClC-5, and ClC-7 (30, 66) and their bacterial homolog,


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Table 2 Nonequilibrium membrane voltages

Physical scenario Schematic ExamplesGoldman–Hodgkin–Katz: multiplepermeable ions, independenttransport of each

A+

B+

Neurons, cardiomyocytes, Purkinje fibers

Goldman with a current source:electrogenic pump

H+ pump: mitochondria (59), Escherichia coli(23), Neurospora crassa (74)

Na+ pump: neutrophils (3), mast cells (9)A+

B+

C+

Cl− pump: epithelial membranes (27), someplant cells (Acetabularia mediterranea) (73)

At the steady state, the net flux of charge is zero, and the net flux of each ion is also zero. The steady-state voltage depends on the i-V relationship of eachcharge transporter, which in turn depends on the detailed molecular mechanism. For each species, the route into the cell may differ from the route out ofit, so detailed balance is not preserved. These voltages require a continuous input of energy. Each reaction scheme is described in detail in the main text.

ClC-ec1 (1). These proteins couple H+ export with Cl− import, resulting in a net export oftwo charge units. The mammalian ClC antiporters reside in intracellular acidifying membranes,whereas ClC-ec1 regulates response to extreme acidity in Escherichia coli (40).

Many other electrogenic transporters have been characterized in detail. The E. coli antiporterNhaA exchanges two H+ ions for one Na+ ion and is important for maintaining a low intracellularsodium concentration in this species (86). Mammalian sodium-calcium exchangers (NCX) couplethe export of one Ca2+ ion with the import of three Na+ ions; these transporters are important inmaintaining low basal concentrations of Ca2+ in neurons and cardiomyocytes (6). Mitochondriahave several electrogenic inner membrane cotransporters: the ATP/ADP exchanger (adeninenucleotide translocator, ANT), the aspartate/glutamate carrier (AGC), and the mitochondrialsodium/calcium exchanger (NCLX) (68). Mitochondria also contain electrogenic transporters ofsingle ions: the calcium uniporter (MCU) and the proton-conducting uncoupling proteins (UCP).

How does one calculate equilibrium membrane voltage for an electrogenic exchanger? Whichway will the exchanger run for a specified membrane voltage and set of ion concentrations? Letus consider the example of the NCX. The reaction is

Ca2+in + 3Na+

out ↔ Ca2+out + 3Na+

in.

The net charge transfer is z = −1 (one positive charge is imported), and there are no chemicaltransformations or redox reactions, so V0 = 0. Thus, the reaction quotient is as follows:

Q = [Na+in]3[Ca2+

out][Na+

out]3[Ca2+in ]

.

One can split the term ln Q in Equation 1 into a sodium-dependent part and a calcium-dependentpart, each of which contains the expression for the Nernst potential of only that ion. Thus,V in−out = (3V Na+ − 2V Ca2+ ), where V Na+ and V Ca2+ are the Nernst potentials of the sodium andcalcium ions, respectively. Note that this formula differs from the Goldman equation discussed be-low, which corresponds to a nonequilibrium situation with independent transport of multiple ions.

Electroneutral exchangers (z = 0) cannot support an equilibrium membrane voltage on theirown. For instance, the mammalian Na-K-Cl cotransporters NKCC1 and NKCC2 import Na+,


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K+, and Cl− in a 1:1:2 stoichiometry and thus transport no net charge (33). However, by modifyingthe current–voltage relations of the individual ions, these exchangers can influence nonequilibriumvoltages (see below). The NKCC cotransporters are found in many mammalian tissues, in whichthey play an important role in regulating osmotic balance. Many of the mitochondrial transportersare also electroneutral. For example, the Pi/H+ carrier (PiC) catalyzes the following reaction:H2PO−

4 out + H+out ↔ H2PO−

4 in + H+in (82).

Redox. Transmembrane electron transfer is well known as a critical aspect of metabolism. Mito-chondria and prokaryotes use transmembrane redox reactions to convert chemical energy into amembrane voltage, which in turn provides part of the proton-motive force that powers the ATPsynthase. Chloroplasts use solar energy to achieve a similar outcome. Yet transmembrane redoxprocesses have also been detected in plasma membranes and intracellular organelles, often playingunanticipated roles. We speculate that redox reactions in membranes are more widespread thanis currently thought.

Cells use plasma membrane electron transport (PMET) to maintain redox homeostasis (insome plant cells), defend against pathogens (in immune cells), and regulate growth (19). For a re-view of PMET in mammalian cells, the reader is referred to Reference 69. The best-documentedexample of mammalian PMET occurs in phagocytes, in which a nicotinamide adenine dinucleo-tide phosphate (NADPH) oxidase mediates transmembrane electron transfer to form superoxide,which kills pathogens (4, 71). The reaction is as follows:

NADPHin + 2O2,out ↔ NADP+in + H+

in + 2O−2,out.

This reaction is electrogenic and has been measured to have an equilibrium potential ofV ≈ +190 mV (20). Here, z = −2 (two electrons exit the cell).

The thermodynamic analysis of transmembrane electron transfer begins, again, withEquation 1. The key new feature is that electrons do not exist in free solution, only bound inmolecules. Thus there can be an energy difference associated with a change in the quantum stateof the electron between reactants and products. This fact introduces a nonzero value for V0 inEquation 1. The standard reduction potential for NADP+ + H+ + 2e− → NADPH is −320 mV(using the biochemical standard state of pH 7) (11), and the standard reduction potential forO2 + e− → O2

− is +160 mV (at [O2] = 1 M) (94). Thus, the standard cell potential, V0, is equalto +160 mV. The equilibrium membrane voltage is given by the following equation:

V in−out = V 0 − RT2F

ln[O−

2,out]2[NADP+

in][O2,out]2[NADPHin]

.

Inside the cell, [NADPH] � [NADP+], whereas outside the cell, [O2] � [O2−]. Both factors drive

the equilibrium voltage more positive than its standard state value.Electron transport across the plasma membrane has also been reported in liver cells (90),

erythrocytes (84), insulin-secreting pancreatic beta cells (31), and the plasma membranes of someplants (thoroughly reviewed in 72). Transmembrane electron transport also occurs in subcellularcompartments. For instance, cytochrome b561 mediates electron transfer across catecholaminesecretory vesicles for the purpose of reducing dopamine to noradrenaline (81). To our knowledge,it is not known whether PMET occurs in canonically active cells such as neurons and cardio-myocytes, or whether glia use it for maintaining redox homeostasis in the brain.

Ion transfer coupled to a chemical reaction. Ion transfer coupled to a chemical reaction thatdoes not involve transmembrane electron transport requires a slightly different analysis. Theparadigmatic example is the F0F1 ATPase, which imports 8 to 14 protons and synthesizes three


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molecules of ATP from ADP and Pi in the process (62). What determines whether the F0F1 ATPsynthase consumes ATP and exports protons or generates ATP and imports protons? The reactioninvolved is as follows:

nH+out + ADPin + Pi,in ↔ nH+

in + ATPin + H2O,

where n is typically between 3 and 4. For simplicity, let us assume n = 4, in which case z = −4. V0 isdetermined by the synthesis of ATP, from the equation V ATP

0 = �r G0zF , where �rG0 = 30.5 kJ/mol

is the standard free energy of reaction for ADP + Pi → ATP (note that this quantity depends onthe concentration of Mg2+ and the pH). Thus V ATP

0 ≈ −80 mV. The reaction quotient is

Q = [H+in]n[ATPin]

[H+out]n[ADPin][Pi,in]

.

This expression simplifies upon expanding the logarithm to obtain the following equation:

V in−outeq = V ATP

0 + 59 mV × �pHin−out − 59n

mV × log QsynthATP .

The pH gradient ranges from 0.5 to 1.2 pH units (the mitochondrial lumen being more basic),thus the second term has a value of 30 to 70 mV (68). The concentrations of ATP, ADP, andPi can vary with metabolic state, but typically, the ratio of mitochondrial [ATP]:[ADP] ≈ 2, and[Pi] ≈ 70 mM (56, 78), yielding log Qsynth

ATP ≈ 1.5. Combining these values, V in−outeq ≈ −70 mV. For

V < Veq, the F0F1 ATP synthase imports protons and produces ATP; for V > Veq, the enzymeexports protons and consumes ATP. As one would hope, the measured membrane voltages implythat mitochondria usually produce ATP.

A similar analysis can be applied to the Na+/K+ ATPase, which maintains the sodium andpotassium concentration gradients needed to sustain electrical activity in neurons and cardiomy-ocytes. The reaction for this protein is

ATP + 3Na+in + 2K+

out → ADP + Pi + 3Na+out + 2K+

in.

As with the ATP synthase, we can estimate how close to thermal equilibrium this enzyme typicallyoperates. Here, z = 1, so V ATP

0 ≈ −320 mV. The reversal potential is

V in−outeq = V ATP

0 + 59 mV × log QhydrATP + 3V Na − 2V K.

For the hydrolysis of ATP, log QhydrATP ≈ −2.5 to −3 at cytoplasmic concentrations ([ATP]:[ADP] ≈

5–10, [Pi] ≈ 10 mM; see Reference 78). In a mammalian neuron, we have VNa = 56 mV andVK = −102 mV. Combining these numbers yields Veq

in−out = −95 to −125 mV. For V > Veq,the Na+/K+ ATPase hydrolyzes ATP, pumps Na+ ions out of the cell, and pumps K+ ions intothe cell; for V < Veq, the enzyme uses ion concentration gradients to synthesize ATP. Neuronstypically have a resting potential near −70 mV. If the resting potential were too close to thereversal potential, then this reaction would proceed too slowly to compensate for the slight Na+

influx and K+ efflux of that accompany each action potential.The membrane potentials with the largest magnitude are found in some plants and fungi, in

which the voltage can approach −300 mV (74). Our thermodynamic analysis above shows that theNa+/K+ ATPase cannot possibly be responsible for this voltage. Rather, these extreme voltageslargely result from the activity of electrogenic ATP-powered proton pumps, which drive thereaction H+

in +ATPin ↔ H+out +ADPin +Pi,in (80). Thermodynamic considerations provide a firm

bound on the membrane voltage. Under basal physiological conditions (not the thermodynamicstandard state), the free energy of ATP hydrolysis is �rG ≈ −45 kJ/mol. The greatest voltage isobtained for export of a monovalent ion, i.e., when z = 1. The pH difference across the membrane


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is small, so Vmax ≈ −460 mV. Because their membrane voltages are large, the first quantitativemeasures of bioelectrical phenomena were obtained from the leaves of the Venus flytrap, Dionaeamuscipula, in 1872 (75). Action potentials were later discovered in the aquatic plant Nitella andmeasured using extracellular electrodes (38).

Donnan. In some cells, the membrane is permeable to all ions except one, often a large polyanionsuch as DNA or RNA. This situation applies to the nuclear envelope (53), vertebrate skeletalmuscle (36), and possibly viral capsids (88). Entropy favors a uniform distribution of the mobileions, but electrostatics requires an excess of mobile cations inside the membrane to offset thecharge of the impermeable polyanions. The competition between entropy and electrostatics leadsto a membrane voltage.

Let us consider the simple case of a polyanion, N −w, with a charge of −w, and a simple salt,KCl, where both the K+ ions and the Cl− ions can freely permeate the membrane. Each permeableion achieves a concentration ratio given by the Nernst equation (Equation 2):

V = RTF

ln[K+

out][K+

in]= −RT

Fln

[Cl−out][Cl−in]

. 3.

We further require overall charge neutrality in the region with the polyanion, so

[Cl−in] + w[N −win ] = [K+

in]. 4.

Finally, the concentrations on the outside are usually clamped by connection to a large reservoir:[Cl−out] = [K+

out] = C0. One can then solve for [Cl−in], [K+in], and V to find

V in−out = −RTF

ln

⎛⎝w[N −w]

2C0+

√(w[N −w]

2C0

)2

+ 1

⎞⎠ . 5.

As an example, we estimate the Donnan potential of the human nuclear envelope. We approximatethe nucleus as a sphere with a diameter of 6 μm. Each of the 6 × 109 base pairs in a diploidcell has two anionic phosphate groups, so the concentration of these anions is approximately200 mM. The ionic strength of cytoplasm, which determines the concentration of mobile charges,is similar; C0 ≈ 150 mM. If DNA were the only membrane-impermeable species, then the Donnanpotential of the nuclear envelope would be approximately −36 mV. However, DNA is wrappedwith positively charged histones, which significantly decrease the mean charge density in thenucleus. Measurements of the nuclear membrane potential give a value of approximately −15 mV(48, 53). The possibility of a Donnan potential in viral capsids has been considered theoretically,but this potential has never been measured experimentally (88).

Donnan potentials can also arise in the absence of a membrane. Simply having a cross-linkedionic hydrogel, such as cartilage, is sufficient. At physiological pH, the proteins that make upcartilage are predominantly negatively charged and have a charge density of approximately200 mM (50). Thus, at physiological ionic strength (C0 ≈ 150 mM), the Donnan potential ofcartilage is approximately −36 mV. As the ionic strength of the solution decreases, its Donnanpotential increases.

Nonequilibrium Membrane Voltages

We have now discussed several diverse sources of membrane voltage at thermal equilibrium. But,equilibrium is death; most biologically interesting systems are far from equilibrium. To createa nonequilibrium situation, one need only establish in the same membrane two independent


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membrane transport processes that have different equilibrium voltages. One process will speedup and the other will slow down until they reach a nonequilibrium steady state at an intermediatevoltage that requires continuous energy input to maintain.

We were able to calculate equilibrium membrane voltages on the basis of thermodynamicprinciples alone, without accounting for the microscopic details of the charge transport processes.For the nonequilibrium systems, however, we are not so lucky. Analyses of these systems requiremicroscopic models of their dynamics and are therefore, by necessity, approximate.

Goldman. When a membrane is permeable to more than one ion, each ion can have a nonzerotransmembrane flux, provided that the net electric current summed over all ions is zero. Massbalance for each ion is achieved by invoking active transporters that counteract the passive fluxbut that do not otherwise appear in the analysis. If one knows how the current for each speciesvaries as the voltage deviates from the equilibrium value for that species, then one can find thevoltage at which the net current is zero.

In the most trivial nonequilibrium model, one might assume that the current for each iongrows linearly as the voltage deviates from its equilibrium value, i.e., i j = σ j (V − Vj ), where σ j isthe conductance for species j and Vj is its Nernst potential. The requirement of no net current isas follows:

∑j i j = 0. In this model, the steady state voltage is simply a weighted average of the

Nernst potentials of each ion, just as we found for the case of concerted cotransport:

V lin =∑

j σ j Vj∑j σ j

.

It is an experimental fact that many ion channels show asymmetric current–voltage relations withgreater apparent conductivity when the current draws ions from the side of the membrane withhigher concentration. This asymmetry is often referred to as rectification. Goldman, Hodgkin,and Katz created a simple model for nonequilibrium ionic transport that reproduces this rectifi-cation behavior. The derivation is given in many textbooks (e.g., 41) and is therefore not repeatedhere. For a voltage dominated by monovalent ions, the Goldman–Hodgkin–Katz equation for thesteady-state voltage is

V = RTF

ln

∑i μi [M +

i ]out + ∑j μ j [M −

j ]in∑i μi [M +

i ]in + ∑j μ j [M −

j ]out, 6.

where μi is the ionic permeability for species i. To preserve the steady-state ionic concentrations,we invoke a metabolically powered pump or exchanger. In neurons, this exchanger is predom-inantly the Na+/K+ ATPase, but the Goldman analysis ignores the electrogenic nature of theNa+/K+ ATPase.

The impact of optogenetically actuated ion channels (e.g., channelrhodopsins) on membranevoltage can be understood in the context of the Goldman equation. Illumination of channel-rhodopsin introduces an additional conductance. The impact of this conductance on voltagedepends on both intracellular and extracellular ionic conditions, as well as the other endogenousmembrane conductances. Depending upon the capacities of endogenous pumps and ion-exchangemechanisms, steady-state activation of a large optogenetic current may also significantly perturbintracellular ion concentrations.

Goldman with a pump. We have seen that when electrogenic charge transport is coupled to achemical reaction, the V0 term in Equation 1 can be significantly larger than the concentration-dependent term. In this case, the equilibrium membrane potential can exceed the diffusion poten-tial of any ion (Equation 2). One often finds an electrogenic chemical reaction occurring in parallel


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with several diffusive charge-transport processes. The voltage in this scenario can be estimatedfrom a revision of the Goldman equation to include a current source.

In the presence of a pump, the sum of the passive electric currents is not zero, but rather∑j i j = −ipump. If one assumes the same ion channel model that led to the Goldman equation,

then the membrane voltage in the presence of a current source is

V = RTF

ln

∑i μi [M +

i ]out + ∑j μ j [M −

j ]in + Jpump∑i μi [M +

i ]in + ∑j μ j [M −

j ]out, 7.

where Jpump is the current density of the current source. Of course, if Jpump is produced by achemically or optically powered protein (as opposed to a patch pipette) then Jpump depends on V.There will exist a so-called stall voltage, at which the value of Jpump goes to zero. However, whenthe pump is operated far from equilibrium, the voltage dependence of Jpump can often be ignored.

Together, electrogenic pumps and passive diffusion determine the membrane voltage in mi-tochondria (V = −150 mV to −190 mV) (63, 68), E. coli (V = −140 mV to −80 mV) (23),neutrophils (3), and mast cells (9). In mitochondria and E. coli, oxidative phosphorylation producesan electrogenic proton current, whereas in mammalian plasma membranes, the most significantelectrogenic pump is typically the Na+/K+ ATPase (which pumps 3 Na+ ions out of the cell andpumps 2 K+ into it). Equation 7 can also be used to model membrane voltage when the electro-genic pump is powered by a photochemical reaction, as occurs in chloroplasts and in membranescontaining microbial rhodopsin charge pumps (e.g., halorhodopsin, archaerhodopsin).

WHY DOES MEMBRANE VOLTAGE MATTER?

Membrane voltage influences every membrane process that involves charge movement. Figure 1illustrates some examples. In each case, the ratio of the population on the left to the populationon the right is given by a Boltzmann distribution:

CL

CR∝ e

− q VkBT , 8.

+ +

+

++

a b c

d e

+

+

–

–

–

–

+

Figure 1Mechanisms by which membrane voltage can influence membrane-associated processes. (a) Voltage gatingof ion channels is well known, but voltage can also affect (b) conformations of proteins other than ionchannels, (c) binding of charged ligands, (d ) concentrations of charged amphiphiles, and (e) distributions ofcharged species within the membrane.


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where q is the amount of charge that moves between the two states, V is the voltage differencethrough which the charge moves, kB is Boltzmann’s constant, and T is the absolute temperature.

The best-known example of voltage regulation is the gating of voltage-dependent ion channels(Figure 1a). These channels are famous for their role in neurons, but bacteria also contain sodiumchannels, inward-rectifier potassium channels, and voltage-gated potassium channels (7, 25), al-though their biological functions are largely unknown (52). Ion channels have been comparativelyeasy to characterize because a voltage-induced conformational change results in a change in theionic current that can be directly measured with an electrode.

However, the role of voltage goes further. Every membrane-bound enzyme, receptor, or trans-porter experiences conformational stresses as a result of membrane voltage pulling on its chargedamino acids. If the protein has multiple conformational states, the balance between these statesis given by Equation 8. Thus, voltage may regulate the activity of the protein, but conventionalelectrode-based measurements may be unable to detect its influence (Figure 1b). The best-knownexample of this phenomenon is the voltage-sensitive phosphatase from Ciona intestinalis, Ci-VSP(61). The voltage-dependent activity of this protein was only demonstrated by coupling its enzy-matic activity to the activation of other ion channels. Unfortunately, this trick does not generalize,so the challenge of identifying cryptic voltage-sensitive transmembrane proteins remains unsolved.However, the default assumption should be that any transmembrane protein is affected by mem-brane voltage; the only question is about the size of the effect for physiological voltage swings.

Membrane voltage can also strongly influence binding interactions in proteins with ligand orion binding sites within the membrane (Figure 1c). For instance, changes in membrane voltagecan tune the acid-base equilibria of titratable groups on the inner segments of transmembraneproteins. This fact is the basis for microbial rhodopsin-based voltage indicators, which undergolarge voltage-dependent shifts in absorption and fluorescence properties (46, 47, 49). These shiftshave been explained by electrical regulation of the acid-base equilibrium of a Schiff base in theprotein core. Multiply charged ligands can be even more sensitive to membrane voltage. Bindingof ATP in the family of ATP binding cassette (ABC) transporters is not likely to be sensitiveto membrane voltage because the ATP-binding domains of these proteins are well outside themembrane. But ligand binding in G protein–coupled receptors (GPCRs) often happens deep inthe protein (29) and thus is plausibly susceptible to membrane voltage.

Membrane voltage regulates transport of membrane-permeable charged species, even in theabsence of specific protein transporters (Figure 1d). Researchers have speculated that most cellshave a negative membrane voltage to facilitate accumulation and retention of amino acids (34).Bacteria are exposed to a wide range of charged amphiphiles, including bile salts and fatty acidsin the intestine, as well as to many drugs and antibiotics. The negative membrane voltage causescationic amphiphiles to accumulate in the cytoplasm. Mitochondria also act as concentrators ofcationic amphiphiles on account of the strongly negative mitochondrial inner membrane voltage.The equilibrium ratio of intracellular to extracellular concentrations is given by Equation 8. Mem-brane voltage can also influence the distribution of charged amphiphiles within the membrane,e.g., by causing lipids to redistribute in a potential-dependent way (Figure 1e).

For a membrane voltage of −120 to −180 mV, the equilibrium concentration of cationicspecies is 100–1,000-fold higher inside the cell than outside it. This fact presents a seriouschallenge for bacteria: To prevent buildup of toxic cationic compounds, bacteria have evolved arange of cationic export machinery. E. coli contain seven distinct efflux systems to combat cationicaccumulation (83). Negative membrane voltages present an energetic barrier to efflux of cationiccontaminants. One plausible explanation for the electrical spiking observed in E. coli is that spikestemporarily remove this electrostatic barrier, facilitating rapid cation efflux. Indeed, pulsatileefflux of a cationic dye was observed to accompany spikes in bacterial membrane potential (47).


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Thus, bacteria may time-share their membrane voltage to accomplish tasks requiring differentdirections of transmembrane charge transport.

Finally, there is evidence that membrane voltage couples directly to the mechanical propertiesof the membrane, particularly its bending modulus. Theoretical analyses have shown that thebending energy of a membrane increases with its surface charge density (92, 93). Remarkably,the outer hair cells involved in hearing show a bidirectional electromechanical coupling: Notonly does deflection induce a voltage, but changes in membrane voltage also directly inducemotion in these cells (10). Atomic force microscopy (AFM) experiments have also observed smallmotions associated with synaptic activation; these motions were attributed to changes in osmoticpressure accompanying activity-induced changes in ionic strength (43). Some researchers have alsosuggested that vesicle-fusion (100) and endocytosis (99) processes may be influenced by membranevoltage directly through a calcium-independent mechanism.

PATCH CLAMP VERSUS OPTOGENETICS

Optogenetic techniques are now widely used to perturb and to measure membrane voltage in cells.Light-gated sodium and calcium channels (channelrhodopsins and their variants) can depolarizea cell and induce firing (8). Light-driven pumps [e.g., halorhodopsins (28) and archaerhodopsins(16)] can hyperpolarize a cell and suppress firing. A palette of genetically encoded voltageindicators can report the response of cells to natural or induced stimuli (2, 65). One may thinkof actuators exposed to brief flashes of light with the primary intent of changing neuronal (orcardiac) firing as being roughly equivalent to a patch electrode. Moreover, indicators that areused to count spikes or to measure action potential waveforms are also roughly equivalent toa patch electrode. However, for biophysical studies, there are subtle but important differencesbetween electrode-based and optical electrophysiology.

Perturbing Membrane Voltage

Whole-cell patch clamp fixes the intracellular concentrations of all ions and small molecules at theconcentrations contained in the patch pipette filling solution. To estimate the time required forcytoplasmic components to equilibrate with a pipette, consider diffusion of a typical small moleculewith a diffusion coefficient D = 200 μm2/s. To diffuse across a cell body with diameter d =20 μm requires a time tD ≈ d2/2D = 1 s. This crude estimate is modified somewhat by the factthat the patch orifice is small compared with the size of the cell, but the d 2/D scaling is robust. Thus,if one is studying the response of a neuron to an extended period of activity or to pharmacologicalperturbations, dialysis of intracellular contents can perturb the results. These perturbations canbe particularly significant for long-term measurements or for measurements on small structures.Indeed, after making a patch clamp connection to a cell, it is quite difficult to remove the pipettewhile keeping the cell alive and to return to the cell on a subsequent day. Cell-attached andperforated patch clamp measurements perturb intracellular contents less than do other techniques,but these techniques are technically demanding and have poorer quality of electrical access.

In contrast, optogenetic approaches preserve the integrity of the cell membrane and therebymaintain endogenous small-molecule and ion dynamics. In their inactive state, optogeneticactuators do not perturb the cytoplasmic content. But when active, these proteins can perturbionic concentrations in ways that patch clamp does not. An optogenetic actuator injects ions of atype determined by the protein’s ionic selectivity, whereas a patch pipette injects ions determinedby the composition of the filling solution. Simply matching steady-state currents does not makeoptogenetic actuators and patch clamp equivalent. Optogenetically pumped ions can reach a steady


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Archz = +1

H+ Na+ 3Na+

3x

Ca2+

H+ Na+ Ca2+

NHEz = 0

NCXz = –1

Ca2+

channelsz = –2

Figure 2Coupled ion-transport processes interact with optogenetic perturbations. This example shows a series ofcoupled processes necessary to achieve mass and charge balance for actuation of a light-gated proton pump.Abbreviations: Arch, Archaerhodopsin 3; NCX, Na+/Ca2+ electrogenic exchanger; NHE, Na+/H+exchanger.

state only by returning to their compartment of origin through another channel or transporter.For example, a light-driven inward chloride pump, halorhodopsin (eNpHR), has been shown toincrease local chloride concentrations sufficiently to change the ion’s equilibrium potential. Thischange shifted the reversal potential of γ-aminobutyric acid (GABA) channels (70).

The effects of other optogenetic actuators can be more subtle. We take as an example Ar-chaerhodopsin 3 (Arch), which generates an outward membrane current, jpump ≈ 10 pA/pF, thatis nearly insensitive to membrane voltage over the physiological range (16). Under steady-stateconditions, this outward current must be balanced by an equal inward proton current. The changein cytoplasmic pH depends on the native permeability of the membrane to protons: If the mem-brane is highly permeable, the change in pH will be small. Consistent with a large basal protonpermeability, Arch-induced changes in pH have been reported to be small (16).

This phenomenon, however, is not the end of the story. Because mammalian neurons transportprotons primarily via the Na+/H+ exchanger (NHE) (98), protons returning to the cell cause Na+

to exit. Furthermore, Na+ efflux is offset by means of the Na+/Ca2+ electrogenic exchanger (NCX).Finally, Ca2+ mass balance is achieved through endogenous calcium channels. Figure 2 shows aplausible set of coupled transport processes that achieve charge and mass balance for each species.This example shows that one must carefully consider downstream ionic perturbations induced byan optogenetic actuator.

Measuring Membrane Voltage

Optical tools are now also being developed to measure membrane voltage. Significant recentadvances have been made in the development of genetically encoded voltage indicators (14, 42, 46)and voltage-sensitive dyes (58, 96). However, one must exercise caution in interpreting data fromthese optical tools as though they were patch clamp measurements: Different tools have differentquirks.

Optical measurements perturb cytoplasmic composition less than do electrical measurements.However, phototoxicity can be a concern, as can the displacement or disruption of endogenous ionchannels by the reporters. Every optical voltage sensor must contain some charge that moves inresponse to changes in membrane voltage. This mobile charge contributes to increased membranecapacitance, which can distort or even suppress action potential waveforms. Capacitive loading issmall in rhodopsin-based protein indicators (49) and molecular wire–based organic dyes (58) butis significant in some hybrid protein/small molecule voltage sensors (15).


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++

+

–

–

–

+ –

+

+

+ +

–

–

–

–

+–+

–Free ions

Tightly boundpositive counterions Dipole

potential

Surfacepotential

Total membranepotential

Transmembranepotential

Loose atmosphere ofnegative counterions

Headgroup

Carbonyl

Figure 3Contributions to the electrical potential profile in a membrane. Charged and dipolar lipid headgroups createa surface potential and a dipole potential, respectively. If either of these quantities is asymmetric across thelipid bilayer, then an electric field may permeate the membrane. This internally generated electric field isundetectable by conventional patch clamp and does not affect equilibrium ionic distributions in the bulk.However, it does act on the conformations of transmembrane proteins and regulates membranepermeability. Adapted with permission from Reference 22.

A more fundamental difference between optical and patch clamp measurements is that they re-port different physical parameters. Optical indicators sense the local electric field in the membrane,whereas patch clamp measurements report the full voltage drop across the membrane and the sur-rounding electrical double layers. These two quantities can differ for several reasons.

Close examination of a lipid membrane shows that the electric field is not homogeneous acrossthe membrane. Indeed, many factors besides the membrane potential contribute to the intramem-brane electric field: The contributions of these factors explain how the activation thresholds ofvoltage-gated ion channels could depend on the lipid or ionic environment. For excellent reviewsof the potential profiles in lipid membranes, the reader is referred to References 17, 54, and 55.Figure 3 shows a typical electrical potential profile across a lipid membrane. Let us consider thecontributions to this profile one at a time.

Surface potential. The surface potential arises from a balance between the tendency of ioniz-able lipid headgroups to dissociate and the resulting electrostatic attraction between the chargedheadgroups and their counterions in solution. Most biological membranes contain a mixture ofanionic and zwitterionic lipids. For example, the surface potential of a typical mammalian plasmamembrane that contains 20% anionic lipids and has an area per lipid headgroup of 60 A2 in a 0.1 Msalt solution is approximately −60 mV relative to the bulk liquid (55). The biological implicationsof this surface potential are discussed in Reference 54.

An asymmetry in the surface potential on opposite sides of a membrane leads to a transmem-brane electric field, even in the complete absence of a macroscopically measurable membrane


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potential. This asymmetry can arise either from differences in the density of anionic lipid head-groups or from differences in the ionic composition of the solutions on opposite sides of themembrane. Monovalent ions (Na+, K+, and Cl−) act primarily by changing the Debye length,and their effect on surface potential can be accounted for within Guoy–Chapman theory. Divalentand higher-valent cations tend to adsorb to the surface, forming a Stern layer, which decreasesthe effective surface charge density. Changes in pH can also affect lipid headgroup ionizationand, thus, the surface charge density. Lipid asymmetry induces local fields that affect ion channelfunction in neurons (5).

Surface potentials can also affect transmembrane ion transport by locally enhancing or depletingion concentrations. For a −60 mV surface potential, the concentration of singly charged cationicspecies at the lipid–solution interface is approximately tenfold greater than in the bulk! Thischange in concentration can affect both the rate at which ions enter the pore of a transporter orchannel and the rates at which small molecules or drugs bind to target receptors in the membrane.

Dipole potential. A second contribution to the voltage profile comes from the so-called dipolepotential (17). This potential arises from oriented dipolar headgroups in zwitterionic lipids andcholesterol at the lipid–solution interface. To appreciate the origin of this potential, one can makean analogy to a parallel plate capacitor: In going from the negatively charged plate to the positivelycharged plate, there is clearly an increase in potential. Now, imagine creating the same chargedistribution by lining up many dipoles in a plane, such that all of their plus ends form one chargesheet and their minus ends form another. Identical charge distributions must lead to identicalpotential profiles.

The dipole potential increases the electrostatic potential inside the membrane. This effectcan be quite large: For example, phosphatidylcholine has a dipole potential of 220–280 mV (18).Cholesterol has been shown to increase the dipole potential and thereby to affect charge-transferrates in the photosynthetic reaction center of Rhodobacter sphaeroides (67). Similar to the surfacepotential, asymmetry in the dipole potential can generate an intramembrane electric field. Thus,if one face of the membrane contains more dipolar species than the opposing face, there will bean electric field in the membrane even in the absence of a macroscopically measurable membranepotential.

Which parameter is correct—the local field or global potential? The answer depends on theprocess being studied. The equilibrium distribution of ions between the bulk phases depends onlyon the global potential difference. In contrast, conformational changes in transmembrane proteinsdepend on the local electric field. Interactions of soluble ions with transmembrane proteins aresensitive to the potential profile in the double layer and in the membrane. Thus, one should notanticipate perfect correspondence between optical and electrode-based voltage measurements.Indeed, differences between local field and global potential have been observed using organicvoltage-sensitive dyes, and these differences may be a means by which neurons generate spatiallyvarying thresholds for ion channel activation (5, 95). Internally generated membrane fields changeslowly compared with the timescale of an action potential, making them difficult to detect withreporters of relative voltage. Reporters of absolute voltage promise to elucidate mechanisms bywhich cells regulate intramembrane electric fields.

THE FUTURE OF OPTICAL ELECTROPHYSIOLOGY

Although one can measure temperature and pH using physical electrodes, fluorescent molecularreporters are often more convenient (57, 97). Similarly, fluorescent molecular reporters facilitatenoninvasive studies of membrane voltage in a dynamic cellular and organismal context. The


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recent progress in the development of small-molecule and genetically encoded voltage reporterssuggests that optical electrophysiology measurements will become routine in the near future.

Unfortunately, brighter, faster, more sensitive voltage indicators will not solve all of the chal-lenges associated with optical electrophysiology. To accommodate the tremendous diversity ofbioelectric phenomena, we must develop new classes of voltage indicators that contain novelmolecular logic. Here, we illustrate three types of molecular logic that are needed.

Reporters of Absolute Voltage

Although most electrophysiology focuses on measuring rapid spikes in membrane voltage, slowshifts in baseline may be equally important. Baseline shifts are likely to regulate membrane trans-port and signaling and are hypothesized to be important in processes such as embryonic develop-ment (85) and wound healing (64), among others.

Reporters that convert membrane voltage directly into changes in fluorescence are good fordetecting fast events such as action potentials. However, these reporters are less useful for measur-ing absolute numerical voltage values or for quantifying slow shifts in baseline voltage because theintensity measurements are confounded by photobleaching, background fluorescence, and vari-ations in reporter concentration and illumination intensity. Patch clamp recordings can reportabsolute voltage during short-term measurements but are not sufficiently stable for long-termmeasurements. Dual-wavelength ratiometric measurements provide some ability to measure ab-solute voltage (5, 95, 101), but this approach requires careful calibration of the optical systemand can be confounded by differential rates of photobleaching and by spectrally inhomogeneousbackground fluorescence.

A common strategy for obtaining accurate measurements is to translate a quantity such asvoltage into the time domain. One could encode voltage information into a time-domain signalin several ways. For electrochromic organic voltage-sensitive dyes (58, 96), the lifetime of theelectronic excited state likely depends on membrane voltage, allowing one- or two-photon fluo-rescence lifetime imaging (FLIM) to be a viable approach to absolute voltage measurements. Asimilar strategy might work for genetically encoded voltage indicators based on circularly per-muted green fluorescent protein (GFP) (42). FLIM will work only if the voltage changes thequantum yield of the electronic excited state, however; this technique will not work if the voltagechanges the ground-state absorption spectrum.

Rhodopsin-based voltage indicators offer an alternate strategy to measure absolute voltage.These proteins have a complex topology of optically and thermally driven transitions, several ofwhich are sensitive to voltage. Thus, if one applies a stepwise change in illumination conditions(either in wavelength or intensity), the protein will relax to a new voltage- and illumination-dependent photostationary state, and in some Archaerhodopsin mutants, e.g., Arch(D95H), thekinetics of this relaxation depend on membrane voltage. The population of the fluorescent statechanges during this relaxation, so the dynamics of the transient fluorescence report the absolutemembrane voltage. For many microbial rhodopsins, relaxation to a photostationary state occursover tens to hundreds of milliseconds, so it can be monitored directly by wide-field imaging (39).

Voltage Integrators and Voltage Samplers

The invention of high-speed voltage indicators created an imaging problem: The moment anaction potential finishes, the accompanying fluorescence signal disappears. Thus, unless one islooking at the neuron when it fires, one misses the event. As a mouse brain contains ∼7.5 ×107 neurons, there is no way to image all of them with sufficient temporal and spatial resolu-tion to record their activity, even using the best voltage indicator conceivable. Neural recording


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requires a data rate of at least 1 kHz. Whole-brain recording therefore requires a data rate of∼1011 bytes/s, which is well beyond the capability of any imaging system. Furthermore, opti-cal scattering prevents real-time optical access to brain regions deeper than ∼1 mm below thesurface.

An alternate strategy is to separate the encoding of the information from its readout. Supposeone could identify a photochemical reaction for which the reaction rate depended on themembrane voltage. Further suppose that the product was fluorescent and the starting materialwas not. One could then deliver a flash of diffuse light to the brain, perhaps paired with astimulus. During the illumination epoch, the rate of photochemical product formation wouldbe proportional to the local neural activity, allowing one to form a permanent photochemicalimprint of activity. This imprint could be read out at a later time, either via slower scanningconfocal imaging or by fixing the brain and slicing or clarifying the tissue. If one can identify aphotochemically reversible reaction with the attributes described above, then one can repeat theprocess multiple times (provided the readout is not terminal).

Although the aforementioned molecular attributes may seem contrived, rhodopsin proteins canachieve this function (89). Many rhodopsins show optical bistability: The retinal in these moietiescan be optically switched between different isomerization states that do not interconvert in thedark (35, 87). We have observed that optical interconversion rates in many rhodopsins are sensitiveto voltage. Thus, naturally occurring or mildly mutated rhodopsins can serve as light-gated voltageintegrators.

A variant on the integrator concept is a light-gated “sample-and-hold.” In some rhodopsins,light of a single wavelength can drive both a forward and reverse isomerization process. In thepresence of light, there is a fast photostationary equilibrium between the isomerization states thatcan be voltage dependent. Thus, the protein may act as a conventional fast voltage indicator inthe light. However, at the moment the illumination turns off, the distributions become fixed andcan therefore be read out at a later time via fluorescence. Such a protein provides an instantaneoussnapshot of neural activity at a moment in time.

One can think of these light-gated voltage reporters as providing a view of neural activityorthogonal to that of conventional patch clamp recordings. Patch clamp typically probes a singleneuron for an extended time; in contrast, these photochemical techniques probe a large numberof neurons—maybe even a complete brain—at a single moment.

CONCLUSION

In this review, we have sought to establish a conceptual framework for optical electrophysiol-ogy and to emphasize that electrophysiology and optogenetics are useful tools for everyone, notjust neuroscientists. Decades of painstaking work by electrophysiologists and biophysicists havedemonstrated a rich diversity of complex interactions of voltage, mechanical forces, ionic currents,and chemical reactions in biological systems. The advent of new optogenetic tools makes it tempt-ing to start prospecting broadly for new bioelectric phenomena, and such prospecting will likely behighly productive. But, amid the bright lights of optical electrophysiology, one should rememberthat all bioelectric phenomena require careful quantitative analysis and that many fundamentalphysical mechanisms remain to be elucidated.

DISCLOSURE STATEMENT

Adam E. Cohen is a founder of Q-State Biosciences.


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Annual Review ofBiophysics

Volume 43, 2014Contents

Fun and Games in Berkeley: The Early Years (1956–2013)Ignacio Tinoco Jr. � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Reconstructing Folding Energy Landscapes by Single-MoleculeForce SpectroscopyMichael T. Woodside and Steven M. Block � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �19

Mechanisms Underlying Nucleosome Positioning In VivoAmanda L. Hughes and Oliver J. Rando � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �41

Microfluidics Expanding the Frontiers of Microbial EcologyRoberto Rusconi, Melissa Garren, and Roman Stocker � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �65

Bacterial Multidrug Efflux TransportersJared A. Delmar, Chih-Chia Su, and Edward W. Yu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �93

Mechanisms of Cellular Proteostasis: Insights fromSingle-Molecule ApproachesCarlos J. Bustamante, Christian M. Kaiser, Rodrigo A. Maillard,

Daniel H. Goldman, and Christian A.M. Wilson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 119

Biophysical Challenges to Axonal Transport: Motor-CargoDeficiencies and NeurodegenerationSandra E. Encalada and Lawrence S.B. Goldstein � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 141

Live Cell NMRDaron I. Freedberg and Philipp Selenko � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 171

Structural Bioinformatics of the InteractomeDonald Petrey and Barry Honig � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 193

Bringing Bioelectricity to LightAdam E. Cohen and Veena Venkatachalam � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 211

Energetics of Membrane Protein FoldingKaren G. Fleming � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 233

The Fanconi Anemia DNA Repair Pathway: Structural and FunctionalInsights into a Complex DisorderHelen Walden and Andrew J. Deans � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 257

vii

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BB43-FrontMatter ARI 15 May 2014 17:38

Angstrom-Precision Optical Traps and ApplicationsThomas T. Perkins � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 279

Photocontrollable Fluorescent Proteins for Superresolution ImagingDaria M. Shcherbakova, Prabuddha Sengupta, Jennifer Lippincott-Schwartz,

and Vladislav V. Verkhusha � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 303

Itch Mechanisms and CircuitsLiang Han and Xinzhong Dong � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 331

Structural and Functional Insights to Ubiquitin-LikeProtein ConjugationFrederick C. Streich Jr. and Christopher D. Lima � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 357

Fidelity of Cotranslational Protein Targeting by the SignalRecognition ParticleXin Zhang and Shu-ou Shan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 381

Metals in Protein–Protein InterfacesWoon Ju Song, Pamela A. Sontz, Xavier I. Ambroggio, and F. Akif Tezcan � � � � � � � � � � � 409

Computational Analysis of Conserved RNA Secondary Structure inTranscriptomes and GenomesSean R. Eddy � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 433

Index

Cumulative Index of Contributing Authors, Volumes 39–43 � � � � � � � � � � � � � � � � � � � � � � � � � � � 457

Errata

An online log of corrections to Annual Review of Biophysics articles may be found athttp://www.annualreviews.org/errata/biophys

viii Contents

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AnnuAl Reviewsit’s about time. Your time. it’s time well spent.

AnnuAl Reviews | Connect with Our expertsTel: 800.523.8635 (us/can) | Tel: 650.493.4400 | Fax: 650.424.0910 | Email: [email protected]

New From Annual Reviews:

Annual Review of Statistics and Its ApplicationVolume 1 • Online January 2014 • http://statistics.annualreviews.org

Editor: Stephen E. Fienberg, Carnegie Mellon UniversityAssociate Editors: Nancy Reid, University of Toronto

Stephen M. Stigler, University of ChicagoThe Annual Review of Statistics and Its Application aims to inform statisticians and quantitative methodologists, as well as all scientists and users of statistics about major methodological advances and the computational tools that allow for their implementation. It will include developments in the field of statistics, including theoretical statistical underpinnings of new methodology, as well as developments in specific application domains such as biostatistics and bioinformatics, economics, machine learning, psychology, sociology, and aspects of the physical sciences.

Complimentary online access to the first volume will be available until January 2015. table of contents:•What Is Statistics? Stephen E. Fienberg•A Systematic Statistical Approach to Evaluating Evidence

from Observational Studies, David Madigan, Paul E. Stang, Jesse A. Berlin, Martijn Schuemie, J. Marc Overhage, Marc A. Suchard, Bill Dumouchel, Abraham G. Hartzema, Patrick B. Ryan

•The Role of Statistics in the Discovery of a Higgs Boson, David A. van Dyk

•Brain Imaging Analysis, F. DuBois Bowman•Statistics and Climate, Peter Guttorp•Climate Simulators and Climate Projections,

Jonathan Rougier, Michael Goldstein•Probabilistic Forecasting, Tilmann Gneiting,

Matthias Katzfuss•Bayesian Computational Tools, Christian P. Robert•Bayesian Computation Via Markov Chain Monte Carlo,

Radu V. Craiu, Jeffrey S. Rosenthal•Build, Compute, Critique, Repeat: Data Analysis with Latent

Variable Models, David M. Blei•Structured Regularizers for High-Dimensional Problems:

Statistical and Computational Issues, Martin J. Wainwright

•High-Dimensional Statistics with a View Toward Applications in Biology, Peter Bühlmann, Markus Kalisch, Lukas Meier

•Next-Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data, Kenneth Lange, Jeanette C. Papp, Janet S. Sinsheimer, Eric M. Sobel

•Breaking Bad: Two Decades of Life-Course Data Analysis in Criminology, Developmental Psychology, and Beyond, Elena A. Erosheva, Ross L. Matsueda, Donatello Telesca

•Event History Analysis, Niels Keiding•StatisticalEvaluationofForensicDNAProfileEvidence,

Christopher D. Steele, David J. Balding•Using League Table Rankings in Public Policy Formation:

Statistical Issues, Harvey Goldstein•Statistical Ecology, Ruth King•Estimating the Number of Species in Microbial Diversity

Studies, John Bunge, Amy Willis, Fiona Walsh•Dynamic Treatment Regimes, Bibhas Chakraborty,

Susan A. Murphy•Statistics and Related Topics in Single-Molecule Biophysics,

Hong Qian, S.C. Kou•Statistics and Quantitative Risk Management for Banking

and Insurance, Paul Embrechts, Marius Hofert

Access this and all other Annual Reviews journals via your institution at www.annualreviews.org.

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